Piecewise linear approximation to Fisher's equation

Zlatko Jovanoski, G. Robinson


A simple method is presented which allows the replacement of a nonlinear differential equation with a piecewise linear differential equation. The method is based on the idea that a curve of the nonlinear terms of the dependent variable in a differential equation can be replaced by an approximate curve consisting of a set of line segments tangent to the original curve. We apply this method to the ubiquitous Fisher's equation and demonstrate that accurate solutions are obtained with a relatively small number of line segments.

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ordinary differential equation; modelling; approximation

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DOI: http://dx.doi.org/10.21914/anziamj.v53i0.5129

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